Dielectric resonances of binary random networks
Résumé
We investigate the AC conductivity of binary random impedance networks, with emphasis on its dependence on the ratio h D 1= 0, with 0 and 1 being the complex conductances of both phases, occurring with respective probabilities p and 1 p. We propose an algorithm to determine the rational h-dependence of the conductance of a finite network, in terms of its poles and of the associated residues. The poles, which lie on the negative real h-axis, are called resonances, since they show up as narrow resonances in the AC conductance of the RL C model of a metal dielectric composite with a high quality factor Q. This approach is an extension of a previous work devoted to the dielectric resonances of isolated finite clusters. A numerical implementation of the algorithm, on the example of the square lattice, allows a detailed investigation of the resonant dielectric response of the binary model, including the p-dependence of the density of resonances and the associated spectral function, the Lifshitz behaviour of these quantities near the endpoints of the spectrum of resonances, the distribution of spacings between neighbouring resonances, and the Q-dependence of the fraction of visible resonances in the RL C model. The distribution of the local electric fields at resonance is found to be multifractal. This result is put into perspective with the giant surface-enhanced Raman scattering observed, for example, in semicontinuous metal films.